Learners’ problem-solving processes in linear programming at selected schools of Lusaka district of Zambia.
Loading...
Date
2024
Authors
Sandambo, Gabriel
Journal Title
Journal ISSN
Volume Title
Publisher
The University of Zambia
Abstract
This study investigated problem-solving processes of Grade 12 learners in linear programming. A total of 24 Grade 12 learners and 2 teachers of Lusaka district of Zambia were purposively sampled for the study from two selected secondary schools. The study employed the qualitative research approach which followed a descriptive case study design. Data was collected using lesson observations, semi-structured interviews and focus group discussions. Thematic analysis was used to analyse data. Polya’s four stages of problem solving: understand the problem, devise the plan(s), execute the plan(s) and looking back, and also the cognitive process dimension of the revised Bloom’s taxonomy guided the analysis of the data. The study
was guided by the following research questions: How do Grade 12 learners engage in solving problems in linear programming? What factors affect Grade 12 learners’ problem-solving processes in linear programming problems? How can Grade 12 learners’ problem-solving processes in linear programming be enhanced? The findings showed that learners in their quest to understand linear programming questions would read the question(s) at least once, though it is not a guarantee for correct solution, they would identify key statements and list phrases with their associated mathematical symbols, and the cognitive demands at this stage were retrieving and recognising factual knowledge. At the devise-a-plan stage, learners were able to transform the conditional statements into inequalities, devise tables of values showing possible pair of coordinates and showed rough-workings. Although, some learners experienced difficulties in comprehending the language of linear programming which led to deriving incorrect inequalities. At this stage, cognitive demands included interpreting and translating the linear programming problem(s) to construct their own meaning and organise facts. At the execute the plan(s) stage, learners could graph the inequalities, identify the feasible region with its boundary points, derive the profit function, test the boundary points into the profit function to determine the pairs of coordinates (x, y) that would yield the max/minimum profit and calculate the maximum/minimum profit. However, some learners experienced difficulties in arriving at correct solutions owing to lack of procedural and conceptual knowledge on how to graph the inequalities and calculating the maximum profit. This stage involved different cognitive levels from Applying through to creating and learners would engage in different cognitive processes from applying inequalities to deriving the feasible region, to evaluating the maximum/minimum profit. The findings further showed that after solving problems in linear programming, learners made little or no effort to engage in a critical examination of the solution arrived at, so as to ascertain whether it is correct and whether the plan can be used to solve another problem(s). At this stage, learners were also operating at the evaluating cognitive level and could engage in the cognitive process of verification and reflection on the problem-solving processes applied for mistake identification and knowledge consolidation. The study showed that learners’ problem-solving processes were constrained by the misunderstanding of the mathematical language of linear programming, poor foundation in pre-requisite knowledge of linear programming, inconsistency of shading the unwanted region at junior and senior secondary levels and lack
of monitoring skills for checking the steps of their solving process affected the learners’ problem-solving processes as they were unable to identify and correct errors and mistakes. To enhance or improve learners’ problem-solving processes, it was suggested that there is need for teachers to be ensuring that learners have the prerequisite knowledge before introducing Linear Programming and there is need for consistency of shading either the unwanted or wanted region at both junior and secondary level to prevent learner misconception. It was further suggested that there is need to promote learner group-working as an approach to teaching linear programming. More learner interaction with authentic and situational problems is another measure that may enhance problem solving process in linear programming.
Description
Thesis of Master of Education in Mathematics Education.